In parallelogram \(ABCD\), let \(O\) be the intersection of diagonals \(\overline{AC}\) and \(\overline{BD}\). Angles \(CAB\) and \(DBC\) are each twice as large as angle \(DBA\), and angle \(ACB\) is \(r\) times as large as angle \(AOB\). Find the greatest integer that does not exceed \(1000r\).

(第十四届AIME1996 第15题)